| The tooth bending strength characteristics of spiral bevel and hypoid gears are investigated in this study both experimentally and theoretically, focusing specifically on the impact of gear alignment errors. On the experimental side, a new experimental set-up is developed for operating a hypoid gear pair under typical load conditions in the presence of tightly-controlled magnitudes of gear misalignments. The test set-up allows application of all four types of misalignments, namely the shaft offset error (V), the horizontal pinion position error (H), the horizontal gear position error (G) and the shaft angle error (gamma). An example face-hobbed hypoid gear pair from an automotive axle unit is instrumented with a set of strain gauges mounted at various root locations of multiple teeth and incorporated with digital signal acquisition and analysis system for collection and analysis of strain signals simultaneously. A number of tests covering typical ranges of misalignments and input torque under both drive and coast conditions are performed to quantify the influence of misalignments on the root stress distributions along the face width.;On the theoretical side, the computational model developed in earlier by Kolivand and Kahraman [31] is expanded to generate the root surfaces of spiral bevel and hypoid gears cut by using either face-milling or face-hobbing processes. A new formulation is proposed to define the gear blank and a numerically efficient cutting simulation methodology is developed to compute the root surfaces from the machine settings, the cutter geometry and the basic design parameters, including both Formate and Generate motions. The generated surfaces are used to define customized finite element models of N-tooth segments of the pinion and the gears via an automated mesh generator. Toot contact loads predicted by a previous load distribution model of Ref. [31] is converted to nodal forces based on the same shape function used to interpolate for nodal displacements. A skyline solver is used to compute the nodal displacements and the resultant stresses at the Gauss points. An extrapolation matrix based on the least-square error formulation is applied to compute the stresses at the root surfaces. Predicted gear root stresses are shown to compare well with the measurements, including not only the extreme stress values but also the stress time histories. Through the same comparisons, the model is also shown to capture the impact of misalignments on the root stress distributions reasonably well.;At the end, a multiaxial, crack nucleation fatigue model of tooth bending is proposed; the model accounts for the multiaxial and non-proportional nature of the stress states predicted. Fatigue lives predicted by the proposed model are compared to those estimated by using a conventional uniaxial failure criterion to show that the predicted multiaxial fatigue lives are significantly lower. The fatigue model is also used to quantify the influence of the misalignments as well as certain key cutting tool parameters on the bending fatigue life of the hypoid gear pair. *Please refer to dissertation for footnotes. |
